Scalarproducts of Spinor Field Functionals and State Representations in Nonlinear Spinor Field Quantum Theory

Abstract

Abstract In preceding papers it was shown that in nonlinear spinor theory cross-sections of elementary particle scattering processes can be calculated only if the state representations and their scalar products are explicitly known. To obtain these quantities, functional quantum theory of the non-linear spinor field was introduced-In this paper it is demonstrated that the introduction of functional scalar products in functional quantum theory is equivalent to impose restrictions to the spinor field operator itself concerning its groundstate behaviour. Performing this, explicit state representations of spinor field states as well as corresponding scalar products can be derived, leading thus to functional quantum theories of the spinor field in dependence on the groundstate model. It follows from these considerations that a spinor field quantum theory is in principle in-complete, as long as no additional assumptions on the groundstate are made, which cannot be derived from the general dynamics of the field.